Related papers: Learning dynamic polynomial proofs
Polynomial regression is a recurrent problem with a large number of applications. In computer vision it often appears in motion analysis. Whatever the application, standard methods for regression of polynomial models tend to deliver biased…
Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…
The motivation of this study is to leverage recent breakthroughs in artificial intelligence research to unlock novel solutions to important scientific problems encountered in computational science. To address the human intelligence…
Deep reinforcement learning enables algorithms to learn complex behavior, deal with continuous action spaces and find good strategies in environments with high dimensional state spaces. With deep reinforcement learning being an active area…
We propose a novel algorithmic framework for distributional reinforcement learning, based on learning finite-dimensional mean embeddings of return distributions. We derive several new algorithms for dynamic programming and…
Dynamical systems are found in innumerable forms across the physical and biological sciences, yet all these systems fall naturally into universal equivalence classes: conservative or dissipative, stable or unstable, compressible or…
The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities by reducing to polynomial inequalities. Finally, we show the great applicability of this algorithm and as examples, we use it to…
Optimizing and certifying the positivity of polynomials are fundamental primitives across mathematics and engineering applications, from dynamical systems to operations research. However, solving these problems in practice requires large…
The key assumption underlying linear Markov Decision Processes (MDPs) is that the learner has access to a known feature map $\phi(x, a)$ that maps state-action pairs to $d$-dimensional vectors, and that the rewards and transitions are…
Reinforcement learning algorithms are defined by their learning update rules, which are typically hand-designed and fixed. We present an evolutionary framework for discovering reinforcement learning algorithms by searching directly over…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
Acquiring mathematical skills is considered a key challenge for modern Artificial Intelligence systems. Inspired by the way humans discover numerical knowledge, here we introduce a deep reinforcement learning framework that allows to…
Univariate polynomial root-finding is a classical subject, still important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the…
Ensuring fairness in machine learning is a critical and challenging task, as biased data representations often lead to unfair predictions. To address this, we propose Deep Fair Learning, a framework that integrates nonlinear sufficient…
Reinforcement learning-based methods for constructing solutions to combinatorial optimization problems are rapidly approaching the performance of human-designed algorithms. To further narrow the gap, learning-based approaches must…
Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…
Being able to reason in an environment with a large number of discrete actions is essential to bringing reinforcement learning to a larger class of problems. Recommender systems, industrial plants and language models are only some of the…
We introduce a theorem proving algorithm that uses practically no domain heuristics for guiding its connection-style proof search. Instead, it runs many Monte-Carlo simulations guided by reinforcement learning from previous proof attempts.…
Deep reinforcement learning is an emerging machine learning approach which can teach a computer to learn from their actions and rewards similar to the way humans learn from experience. It offers many advantages in automating decision…
Deep reinforcement learning is an increasingly popular technique for synthesising policies to control an agent's interaction with its environment. There is also growing interest in formally verifying that such policies are correct and…